Kurt Gödel's incompleteness theorem is sometimes alleged to undermine the purpose of the project. (However, one can argue that the basic spirit of Logicism remains valid, though in a somewhat less powerful sense than was originally thought.)

Neo-logicism

Neo-logicism describes a range of views claiming to be the successor of the original logicist program. More narrowly, it is defined as attempts to resurrect Frege's programme through the use of Hume's Principle. Two of the major proponents of neo-logicism are Crispin Wright and Bob Hale.